The Great Mind-Boggling Antifreeze Mixture

Jan 16, 2006

RAY: I got this puzzler just recently from a young gal named Rosie Stephan. Time was of the essence, so I decided to use it. She writes:

"Hi guys, my name is Rosie, and I'm 14 years old. My father Rich and I have been listening to your show every Saturday for, well, as long as I can recall. Now, it is nearing the dreaded time in every father's life when his teenage daughter is about to turn 16. It's going to be hell and he knows it. So he's trying desperately to find a way to stall for time. This evening, he gave me this scenario: I can have my license at 16, if I can figure out the following problem."

So, obviously she's been unable to figure it out, so she's asking us, and if our listeners solve it, she's going to get her license.

TOM: That's not fair.

RAY: What do we care? All's fair in love and puzzlers! She continues, "My car's cooling system holds 12 quarts." Note how she refers to it as "my car," and she doesn't even have her license yet!

"Right now it has four quarts of antifreeze, and eight quarts of water. How much of this mixture do I have to drain out and replenish with straight antifreeze in order to get a 50/50 mixture? Please come to my aid. My life depends on it!"

I thought I would add a "Part B" to this puzzler. How much of this mixture do I have to drain out if I'm adding antifreeze that's already been mixed 50/50 to get a 50/50 mix?

Answer:

RAY: You could write equations for all this, or you could do it the easy way. The easy way is to say you've got 12 quarts, so four of them are antifreeze and eight of them are water.

So, if you have a one third mixture that means if you took three quarts of that mixture out, two of them would be water and one of them would be antifreeze. You're going to wind up with three quarts of antifreeze and six quarts of water, are you not?

TOM: Right.

RAY: If you now add three quarts of pure antifreeze back you'll have six quarts of antifreeze and --

TOM ANDRAY: Six quarts of water!

RAY: You drain out three quarts of the mixture. That's the answer to part A. Now, for part two: how much of this mixture do you have to drain out if you want to get to 50% water and 50% coolant, if you're adding a 50/50 mixture of water and antifreeze?

TOM: You can't.

RAY: Right. You have to drain out all 12 quarts in order for it to work. Do we have a winner?

TOM: The winner is Ryan Fall from Sandy, Utah. And for having his answer selected at random from among all the correct answers that we got, Ryan gets a 26-dollar gift certificate to the Shameless Commerce Division at cartalk.com where he can sweep through the aisles of our virtual Car Talk supermarket and grab all of the Car Talk junk that he wants, up to a limit of course of 26 bucks.